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Nonparametric Regression Estimation for Random Fields in a Fixed-Design

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Abstract

We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These estimators can attain the optimal rates of uniform convergence and the results apply to a large class of random fields which contains martingale-difference random fields and mixing random fields.

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Correspondence to Mohamed El Machkouri.

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Articlenote: In final form 24 January 2005

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Machkouri, M.E. Nonparametric Regression Estimation for Random Fields in a Fixed-Design. Stat Infer Stoch Process 10, 29–47 (2007). https://doi.org/10.1007/s11203-005-7332-6

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AMS Mathematics Subject Classification (2000):

  • 60G60
  • 62G08

Keywords

  • nonparametric regression estimation
  • kernel estimators
  • strong consistency
  • fixed-design
  • exponential inequalities
  • martingale difference random fields
  • mixing
  • Orlicz spaces